Let \(\xi _{j,m}^{n_{j}}\)  denote the complex channel gain between the \(n_{j}\) -th reflecting element of IRS \(j\)  and the \(m\) -th antenna at the BS. Since the sizes of each IRS reflecting element and antenna element are of sub-wavelength, the UPW assumption still holds for the LoS channel between any two IRS/antenna elements, despite their short distance [1]}. As such, we have
\(\xi _{j,m}^{n_j}=\frac{\lambda }{4\pi ||\mbox{{$ s $}}_{m}-\mbox{{$ w $}}_{j,n_{j}}||}e^{-i\frac{2\pi }{\lambda }||\mbox{{$ s $}}_{m}-\mbox{{$ w $}}_{j,n_{j}}||}.\) 
